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New results are presented on a high-statistics measurement of Collins andSivers asymmetries of charged hadrons produced in deep inelastic scattering ofmuons on a transversely polarised $^6$LiD target. The data were taken in 2022with the COMPASS spectrometer using the 160 \gevv\ muon beam at CERN, balancingthe existing data on transversely polarised proton targets. The first resultsfrom about two-thirds of the new data have total uncertainties smaller by up toa factor of three compared to the previous deuteron measurements. Using all theCOMPASS proton and deuteron results, both the transversity and the Siversdistribution functions of the $u$ and $d$ quark, as well as the tensor chargein the measured $x$-range are extracted. In particular, the accuracy of the $d$quark results is significantly improved.

High-statistics measurement of Collins and Sivers asymmetries for transversely polarised deuterons